$J$ $K$ $L$ If: $ KL = 6x + 8$, $ JL = 68$, and $ JK = 8x + 4$, Find $KL$.
Solution: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {8x + 4} + {6x + 8} = {68}$ Combine like terms: $ 14x + 12 = {68}$ Subtract $12$ from both sides: $ 14x = 56$ Divide both sides by $14$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $KL$ $ KL = 6({4}) + 8$ Simplify: $ {KL = 24 + 8}$ Simplify to find ${KL}$ : $ {KL = 32}$